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It was recently proposed inhttps://journals.aps.org/pre/abstract/10.1103/PhysRevE.94.043322 [Herdeiro &Doyon Phys.,Rev.,E (2016)] a numerical method showing a precise sampling of theinfinite plane 2d critical Ising model for finite lattice subsections. Thepresent note extends the method to a larger class of models, namely the $O(n)$loop gas models for $n \in (1,2]$. We argue that even though the Gibbs measureis non local, it is factorizable on finite subsections when sufficientinformation on the loops touching the boundaries is stored. Our results attemptto show that provided an efficient Markov chain mixing algorithm and animproved discrete lattice dilation procedure the planar limit of the $O(n)$models can be numerically studied with efficiency similar to the Ising case.This confirms that scale invariance is the only requirement for the presentnumerical method to work.

Markov chain sampling of the $O(n)$ loop models on the infinite plane